3/4x=-8/9x-400

Solution for 3/4x=-8/9x-400 equation:

3/4x=-8/9x-400

We move all terms to the left:

3/4x-(-8/9x-400)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 9x-400)!=0

x∈R


We get rid of parentheses

3/4x+8/9x+400=0

We calculate fractions


27x/36x^2+32x/36x^2+400=0

We multiply all the terms by the denominator


27x+32x+400*36x^2=0

We add all the numbers together, and all the variables

59x+400*36x^2=0

Wy multiply elements

14400x^2+59x=0

a = 14400; b = 59; c = 0;
Δ = b2-4ac
Δ = 592-4·14400·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-59}{2*14400}=\frac{-118}{28800}
=-59/14400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+59}{2*14400}=\frac{0}{28800}
=0
$